Re: triangles in circles

*To*: mathgroup at smc.vnet.net*Subject*: [mg26856] Re: [mg26813] triangles in circles*From*: Andrzej Kozlowski <andrzej at bekkoame.ne.jp>*Date*: Thu, 25 Jan 2001 01:13:32 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

Here is some quickly written code that will create the points on the circle and the triangles you want. I make use of the Combinatorica package to construct all the choices of three points out of n. First we load the package: << DiscreteMath`Combinatorica` Next we get the coordinates of the points on the unit circle: pts[n_] := {Re[#], Im[#]} & /@ Map[ExpToTrig, Table[E^(2Pi*I*k/n), {k, 1, n}]] Here are the triangles that can be made given n-points (n>2). triangles[n_] := Line /@ KSubsets[pts[n], 3] /. Line[a_] :> Line[Append[a, First[a]]] You can see them with: Show[Graphics[{triangles[7]}], AspectRatio -> Automatic] This can be improved in various ways, by adding the ciorcle, colour etc. -- Andrzej Kozlowski Toyama International University JAPAN http://platon.c.u-tokyo.ac.jp/andrzej/ http://sigma.tuins.ac.jp/ on 1/24/01 6:18 PM, Tom De Vries at tdevries at shop.westworld.ca wrote: > Hello all, > > I'm teaching a high school math class and we are doing permutations and > combinations. One of the "standard" questions is ..."given a certain number > of points located around a circle, how many triangles can be formed...." > > The simple line below creates a circle with 5 points arranged around it. > Could someone help me with a way to generate the lists of points that would > create all the triangles. I know that for more points it would get kind of > messy, but I wanted to actually draw all the triangles as I thought it might > be an interesting graphic... > > Thanks for any help you might have.... > > > n = 5; > > ptlist = Table[{Cos[i 2 \[Pi]/n], Sin[i 2 \[Pi]/n]}, {i, 1, n}]; > > Show[Graphics[{ > Circle[{0, 0}, 1], > {PointSize[0.02], Point /@ ptlist} > }], AspectRatio -> Automatic] > > Sincerely, Tom De Vries > > >